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August 27th, 2016, 04:03 PM   #1
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calculate angle x

In the figure, AB=AC and HN=MN. Calculate measure of angle x.123.jpg
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Answer x=90°

Last edited by skipjack; October 28th, 2018 at 10:00 PM.
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August 28th, 2016, 06:16 PM   #2
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You posted 8 problems, but showed no attempts at solutions.

Are you trying to get your homework done here?

Concerning this problem, since posted in "Geometry section",
is it assumed that no trigonometry is allowed?
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August 28th, 2016, 07:20 PM   #3
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Quote:
Originally Posted by Nathalia View Post
In the figure, AB=AC and HN=MN. Calculate measure of angle x.Attachment 7905
Thank you.

Answer x=90°
In general, this is not true. Move point $\displaystyle M$ closer to point $\displaystyle C$ and the angle $\displaystyle X$ becomes obtuse.

Last edited by skipjack; October 28th, 2018 at 10:01 PM.
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August 28th, 2016, 08:25 PM   #4
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In general, this is not true. Move point $\displaystyle M$ closer to point $\displaystyle C$ and the angle $\displaystyle X$ becomes obtuse.
You mean "only works when point M is at center of BC", right?

Last edited by skipjack; October 28th, 2018 at 10:01 PM.
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August 29th, 2016, 07:54 AM   #5
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Quote:
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You mean "only works when point M is at center of BC", right?
Yes, that is what I meant. Even though I was born and educated in the U.S., in school I took English as a foreign language.

Last edited by skipjack; October 28th, 2018 at 10:02 PM.
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August 29th, 2016, 09:06 AM   #6
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...in school I took English as a foreign language.
So did I: mother tongue = French.
Dad Irish, Mom French...and the BOSS!!
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October 28th, 2018, 03:09 PM   #7
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Let I be the point of intersection of (AN) and (HC)
angle AMN = angle (HBC) ...... (1)
BM/AM = BH/HM THEN
2(BM/AM) = BH/(HM/2)
OR BC/AM = BH/MN
SO BC/BH = AM/MN ........ (2)
(1) AND (2) MEANS THAT THE 2 TRIANGLES CBH AND AMN ARE SIMILAR AND ANGLE NAM = ANGLE HCB
THEREFORE THE QUADRILATERAL AIMC IS CYCLIC AND x = 90°

Last edited by skipjack; October 29th, 2018 at 12:15 AM.
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